CN110532867B - Facial image clustering method based on golden section method - Google Patents

Abstract

A facial image clustering method based on a golden section method comprises the following steps: 1) applying a DCNN (deep convolutional neural network) to realize the characteristic representation of all face pictures in a database; 2) clustering the image representations by applying a K-Means + + clustering algorithm; 3) determining the optimal clustering number based on a 0.618 golden section method, wherein the process comprises the following steps: first, a clustering range [ a, b ] is given]，K∈[a,b]. Arbitrarily initializing a given number of clusters K within a range₀Establishing an optimization function f (K) based on the internal performance evaluation indexes of the clustering result; then, based on the golden section optimization algorithm of 0.618, one-dimensional dynamic search function optimal solution is carried out. The optimal solution is the optimal clustering number K^*Corresponding to the clustering result C^*The best cluster of the facial image library is obtained. The invention obviously improves the face image clustering performance.

Description

Facial image clustering method based on golden section method

Technical Field

The invention relates to a face image clustering method, in particular to a face image clustering method based on a golden section method.

Background

With the rapid development of computer vision and pattern recognition technology, images have wide application prospects as the most common visual information presentation mode. In the "big data" era, a large number of pictures are produced every day. For example, Facebook reports on social media produce an average of 3.5 million pictures per day, most of which are images of human faces. In judicial investigation, there is still a huge number of pictures that need to be identified and classified urgently. In social security maintenance and monitoring management, a large number of face images captured by the camera need to be subjected to identity authentication and warehousing comparison. However, these face images usually have no identity tag or the tag is lost. In the face of such a huge image database, it is difficult to ensure the accuracy and effectiveness of identification by using the manual labeling method, and the method is time-consuming and labor-consuming.

The rise of machine learning provides an effective solution to this troublesome problem. In recent years, the deep convolutional neural network DCNN shows excellent performance in image feature extraction and identity recognition: according to the current research at home and abroad, the recognition performance of the method far exceeds that of human eyes. Meanwhile, the data clustering technology is mature day by day, and a method basis is provided for solving the problems of large-scale image data identification and classification. However, applying the clustering technique requires giving the number of image clusters in advance. Typically, facing large image databases, the number of clusters can be hundreds or thousands or even difficult to determine.

Disclosure of Invention

The invention provides a facial image clustering method based on a golden section method, aiming at overcoming the defect of poor performance of the existing facial image clustering method and obviously improving the facial image clustering performance.

The technical scheme adopted by the invention for solving the technical problems is as follows:

a facial image clustering method based on a golden section method comprises the following steps:

1) the method is characterized by comprising the following steps of applying a DCNN (deep convolutional neural network) to realize the characteristic representation of all face pictures in a database:

step 1.1: the preprocessing is to perform preliminary correction processing on the image;

step 1.2: accurately positioning a face region in the image and cutting the region based on 68 feature points labeled by the Dlib face;

step 1.3: extracting the characteristics of the cut face by applying pre-trained DCNN (Dlib ResNet), and outputting a 128-dimensional characteristic vector as the representation of the face;

2) the clustering of the image representation is realized by applying a K-Means + + clustering algorithm, and the operation steps are as follows:

step 2.1: set X ═ where face representations are represented in the form of a column matrix (X)₁,X₂,···,X_n) Wherein X is a 128-dimensional face representation, and n is the number of faces;

step 2.2: giving a clustering number K, and randomly initializing and selecting a representation as a clustering center point;

step 2.3: for each X_i(X_iE.g. X), calculating its euclidean distance D (X) to the nearest cluster center point_i) And calculates the sum of all distances

Step 2.4: a random number κ is generated within the range of sumd (x). The following criteria were used: k ═ D (X)_i) The next cluster center is selected until κ < 0, thus resulting in a larger D (X)_i) The characterization point of (2) has higher probability to be selected as the next clustering center point;

step 2.5: repeating the steps 2.3 to 2.4 until K cluster center points (U)₁,U₂,···,U_K) Finishing the selection;

step 2.6: calculating each face representation X_iWith each initialized cluster center U_jEuclidean distance of (a):

step 2.7: according to minimum D_ijDetermination of X_iCluster marking of (2): lambda [ alpha ]_i＝argmin_{j∈{1,2,···,K}}D_ij；

Step 2.8: mixing X_i Dividing into corresponding clusters:

step 2.9: calculating a new clusterClass center

And replaces the original clustering center U_j；

Step 2.10: repeating step 2.6 to step 2.9 until U_j ^*＝U_j；

Step 2.11: outputting the cluster division result C ═ { C ═ C₁,C₂,···,C_K}；

3) Determining the optimal clustering number based on a 0.618 golden section method, wherein the process comprises the following steps: first, a clustering range [ a, b ] is given]，K∈[a,b]. Arbitrary initialization of the number of clusters K within the range₀Establishing an optimization function f (K) based on the internal performance evaluation indexes of the clustering result; then, based on the 0.618 golden section optimization algorithm, one-dimensional dynamic search function optimal solution is obtained, and the optimal solution is the optimal clustering number K^*Corresponding to the clustering result C^*The best cluster of the facial image library is obtained.

Further, in the step 3), the dynamic searching step is as follows:

calculating the corresponding output value f (K) of the DBI coefficient as the optimization function about K, and dividing C ═ C corresponding to the cluster₁,C₂,···,C_KThe process is represented as:

wherein, each parameter and function realization are defined as follows:

k: the number of clusters;

avg (C): characterizing the mean value of faces in the cluster;

l C |: the number of face tokens in cluster C;

D_U(C_i,C_j)：C_iand C_jCenter distance between clusters;

u: the center of cluster C;

because the DBI coefficients of different clustering results generated by different Ks can be calculated, an optimal objective function f (K) related to the K and an optimal clustering number K can be constructed^*Necessarily corresponding to the minimum DBI value, and therefore f (K) may be at K^*Neighborhood of [ a, b ]]Taking the method as a unimodal function, the searching steps by applying the golden section method of 0.618 are as follows:

step 3.1: given an initial cluster number range [ a ]₀,b₀]Error condition epsilon;

step 3.2: calculating lambda₀＝a₀+0.382(b₀-a₀),μ₀＝a₀+0.618(b₀-a₀)；

Step 3.3: calculating function value f₁＝f([λ_k]) And f₂＝f([μ_k]) Wherein the variable value is rounded down;

step 3.4: if b is_k-a_kIf not more than epsilon, ending the search; if b is_k-a_kIf the value is more than epsilon, turning to the step 3.5;

step 3.5: if f is₁＞f₂If yes, go to step 3.6; if f₁＜f₂Then go to step 3.7;

step 3.6: a is_k+1＝λ_k,b_k+1＝b_k,λ_k+1＝μ_k,μ_k+1＝a_k+1+0.618(b_k+1-a_k+1). Calculating function value f₂＝f([μ_k+1]) Go to step 3.8;

step 3.7: a is_k+1＝a_k,b_k+1＝μ_k,μ_k+1＝λ_k,λ_k+1＝a_k+1+0.382(b_k+1-a_k+1). Calculating function value f₁＝f([λ_k+1]) Go to step 3.8;

step 3.8: setting k: go to step 3.4 when k + 1;

the cluster number range obtained finally by the one-dimensional search is recorded as [ a ]_k,b_k]Therefore, the median value in this range is taken as the optimal cluster number:

the optimal cluster number is rounded down.

The technical conception of the invention is as follows: under the current background of the "big data" era, a large amount of unidentified face images are generated in many fields such as social media, judicial survey and the like. In order to solve the problem of face identity recognition and classification of a large-scale face image database, an effective solution is provided by combining a DCNN and a K-Means + + clustering algorithm. Firstly, the representation of the face image is realized by adopting DCNN. And then, identifying and classifying the obtained face representation by applying a K-Means + + clustering algorithm. In the face of the clustering task of large-scale databases, the reasonable number of clusters is often unknown and difficult to determine. In this regard, a method for one-dimensional dynamic search of the optimal cluster number based on the 0.618 golden section method is proposed. The method can effectively search and find out reasonable clustering number, thereby improving clustering performance.

The beneficial effects of the invention are mainly as follows: 1. in order to solve the problem of image recognition and classification in a large-scale face image database, an image clustering method based on DCNN and K-Means + + algorithm is provided. The method realizes face representation by applying DCNN, and can ensure the accuracy and effectiveness of recognition. 2. And dynamically searching the optimal clustering number by applying a 0.618 golden section algorithm, thereby solving the problem that the most important clustering number in the clustering task is unknown. The solution of this problem can greatly improve the performance of clustering, and the application of this search method will not excessively increase the complexity of computation and time loss, and is therefore suitable for image clustering of large-scale databases.

Drawings

FIG. 1 is a schematic diagram of a DCNN-based face image representation implementation;

FIG. 2 is a flow chart of the K-Means + + algorithm;

fig. 3 is a flow chart of the golden section algorithm.

Detailed Description

The present invention is described in further detail below with reference to the attached drawing figures.

Referring to fig. 1 to 3, a facial image clustering method based on the golden section method includes 3 parts: the method comprises the steps of characterizing facial images by applying DCNN (as shown in figure 1), identifying and classifying a large number of facial features by using a K-Means + + clustering algorithm (as shown in figure 2), and searching for the optimal clustering number in one dimension by using a golden section algorithm (as shown in figure 3), thereby improving the clustering performance. The method comprises the following steps:

1) the method is characterized in that a Deep Convolutional Neural Network (DCNN) is applied to realize the feature representation of all face pictures in a database, the process comprises preprocessing, face alignment and feature extraction, and the steps are as follows:

step 1.1: the preprocessing is to perform preliminary correction processing on the image, for example, the social media picture needs to be subjected to brightness equalization processing, the biomedical material picture needs to be subjected to denoising processing, and the like. The pretreatment can obviously improve the performance of feature extraction;

step 1.2: accurately positioning a face region in the image and cutting the region based on 68 feature points labeled by the Dlib face;

step 1.3: extracting the characteristics of the cut face by applying pre-trained DCNN (Dlib ResNet), and outputting a 128-dimensional characteristic vector as the representation of the face;

2) the clustering of the image representation is realized by applying a K-Means + + clustering algorithm, and the operation steps are as follows:

step 2.1: set X ═ where face representations are represented in the form of a column matrix (X)₁,X₂,···,X_n) Wherein X is the human face representation with 128 dimensionality, and n is the number of human faces;

step 2.2: giving a clustering number K, and randomly initializing and selecting a representation as a clustering center point;

step 2.3: for each X_i(X_iE.g. X), calculating its euclidean distance D (X) to the nearest cluster center point_i) And calculates the sum of all distances

Step 2.4: a random number κ is generated within the range of SumD (X). The following criteria were used: k-D (X)_i) Until k < 0, the next cluster center is selected, thus resulting in a larger D (X)_i) The characterization point of (2) has higher probability to be selected as the next clustering center point;

step 2.5: repeating the steps 2.3 to 2.4 until K cluster center points (U)₁,U₂,···,U_K) Finishing the selection;

step 2.6: calculating each face representation X_iWith each initialized cluster center U_jEuclidean distance of (a):

step 2.7: according to minimum D_ijDetermination of X_iCluster marking of (2): lambda [ alpha ]_i＝argmin_{j∈{1,2,···,K}}D_ij；

Step 2.8: mixing X_i Dividing into corresponding clusters:

step 2.9: computing new cluster centers

And replaces the original clustering center U_j；

Step 2.10: repeating step 2.6 to step 2.9 until

Step 2.11: output cluster division result C ═ C₁,C₂,···,C_K}；

3) Determining the optimal clustering number based on a 0.618 golden section method, wherein the process comprises the following steps: first, a clustering range [ a, b ] is given]，K∈[a,b]. Arbitrarily initializing a given cluster number K within a range₀Internal performance evaluation index construction optimization based on clustering resultsA change function f (K); then, based on the 0.618 golden section optimization algorithm, one-dimensional dynamic search function optimal solution is obtained, and the optimal solution is the optimal clustering number K^*Corresponding to the clustering result C^*The best cluster of the facial image library is obtained.

Further, in the step 3), the dynamic searching step is as follows:

calculating the corresponding output value f (K) of the DBI coefficient as the optimization function about K, and dividing C ═ C corresponding to the cluster₁,C₂,···,C_KThe process is represented as:

wherein, each parameter and function realization are defined as follows:

k: the number of clusters;

avg (C): characterizing the mean value of faces in the cluster;

l C |: the number of face tokens in cluster C;

D_U(C_i,C_j)：C_iand C_jCenter distance between clusters;

u: the center of cluster C;

because the DBI coefficients of different clustering results generated by different Ks can be calculated, an optimal objective function f (K) related to the K and an optimal clustering number K can be constructed^*Necessarily corresponding to the minimum DBI value, and therefore f (K) may be at K^*Neighborhood of [ a, b ]]Taking the method as a unimodal function, the searching steps by applying the golden section method of 0.618 are as follows:

step 3.1: given an initial cluster number range [ a ]₀,b₀]Error condition epsilon;

step 3.2: calculating lambda₀＝a₀+0.382(b₀-a₀),μ₀＝a₀+0.618(b₀-a₀)；

Step 3.3: calculating function value f₁＝f([λ_k]) And f₂＝f([μ_k]) Wherein the variable value is rounded down;

step 3.4: if b is_k-a_kIf not more than epsilon, ending the search; if b is_k-a_kIf the value is more than epsilon, turning to the step 3.5;

step 3.5: if f is₁＞f₂Then go to step 3.6; if f₁＜f₂Then go to step 3.7;

step 3.6: a is_k+1＝λ_k,b_k+1＝b_k,λ_k+1＝μ_k,μ_k+1＝a_k+1+0.618(b_k+1-a_k+1). Calculating function value f₂＝f([μ_k+1]) Go to step 3.8;

step 3.7: a is_k+1＝a_k,b_k+1＝μ_k,μ_k+1＝λ_k,λ_k+1＝a_k+1+0.382(b_k+1-a_k+1). Calculating a function value f₁＝f([λ_k+1]) Go to step 3.8;

step 3.8: setting k: go to step 3.4 when k + 1;

the cluster number range obtained finally by the one-dimensional search is recorded as [ a ]_k,b_k]Therefore, the median value in this range is taken as the optimal cluster number:

the optimal cluster number is rounded down.

Claims (1)

1. A facial image clustering method based on a golden section method is characterized by comprising the following steps:

1) the method is characterized by comprising the following steps of applying a DCNN (deep convolutional neural network) to realize the characteristic representation of all face pictures in a database:

step 1.1: the preprocessing is to perform preliminary correction processing on the image;

step 1.2: accurately positioning a face region in the image and cutting the region based on 68 feature points labeled by the Dlib face;

step 1.3: extracting the features of the cut human face by using the pre-trained DCNN, and outputting a 128-dimensional feature vector as the representation of the human face;

2) the clustering of the image representation is realized by applying a K-Means + + clustering algorithm, and the operation steps are as follows:

step 2.1: set X ═ where face representations are represented in the form of a column matrix (X)₁,X₂,···,X_n) Wherein X is the human face representation with 128 dimensionality, and n is the number of human faces;

step 2.2: giving a clustering number K, and randomly initializing and selecting a representation as a clustering center point;

step 2.3: for each X_i，X_iE.g. X, calculating the Euclidean distance D (X) from the nearest cluster center point_i) And calculates the sum of all distances

Step 2.4: a random number k is generated within the range of sumd (x), using the following criteria: k ═ D (X)_i) The next cluster center is selected until κ < 0, thus allowing for a larger D (X)_i) The characterization point of (2) has higher probability to be selected as the next clustering center point;

step 2.5: repeating the steps from 2.3 to 2.4 until K cluster center points (U)₁,U₂,···,U_K) Finishing the selection;

step 2.6: calculating each face representation X_iWith each initialized cluster center U_jEuclidean distance of (c): d_ij＝||X_i-U_j||₂；

Step 2.7: according to minimum D_ijDetermination of X_iCluster marking of (2): lambda_i＝arg min_{j∈{1,2,···,K}}D_ij；

Step 2.8: mixing X_i Dividing into corresponding clusters:

step 2.9: computing new cluster centers

And replaces the original clustering center U_j；

Step 2.10: repeating step 2.6 to step 2.9 until

Step 2.11: outputting the cluster division result C ═ { C ═ C₁,C₂,···,C_K}；

3) Determining the optimal clustering number based on a 0.618 golden section method, wherein the process comprises the following steps: first, a clustering range [ a, b ] is given]，K∈[a,b]Arbitrarily initializing a given number of clusters K within the range₀Establishing an optimization function f (K) based on the internal performance evaluation indexes of the clustering result; then, based on the 0.618 golden section optimization algorithm, one-dimensional dynamic search function optimal solution is obtained, and the optimal solution is the optimal clustering number K^*Corresponding to the clustering result C^*The best cluster of the face image library is obtained;

in the step 3), the dynamic searching step is as follows:

calculating the corresponding output value f (K) of the DBI coefficient as the optimization function about K, and dividing C ═ C corresponding to the cluster₁,C₂,···,C_KThe process is represented as:

D_U(C_i,C_j)＝||U_i-U_j||₂

wherein, each parameter and function realization are defined as follows:

k: the number of clusters;

avg (C): characterizing the mean value of faces in the cluster;

l C |: the number of face tokens in cluster C;

D_U(C_i,C_j)：C_iand C_jThe center distance between clusters;

u: the center of cluster C;

because the DBI coefficients of different clustering results generated by different Ks can be calculated, an optimal objective function f (K) related to the K is constructed, and the optimal clustering number K^*Necessarily corresponding to the minimum DBI value, and therefore f (K) at K^*Neighborhood of [ a, b ]]Taking the interior as a unimodal function, the searching steps by applying the golden section method of 0.618 are as follows:

step 3.1: given an initial cluster number range [ a ]₀,b₀]Error condition epsilon;

step 3.2: calculating lambda₀＝a₀+0.382(b₀-a₀),μ₀＝a₀+0.618(b₀-a₀)；

Step 3.3: calculating function value f₁＝f([λ_k]) And f₂＝f([μ_k]) Wherein the variable value is rounded down;

step 3.4: if b is_k-a_kIf the epsilon is less than or equal to epsilon, ending the search; if b is_k-a_kIf the value is more than epsilon, turning to the step 3.5;

step 3.5: if f is₁＞f₂Then go to step 3.6; if f₁＜f₂Then go to step 3.7;

step 3.6: a is a_k+1＝λ_k,b_k+1＝b_k,λ_k+1＝μ_k,μ_k+1＝a_k+1+0.618(b_k+1-a_k+1) Calculating a function value f₂＝f([μ_k+1]) Go to step 3.8;

step 3.7: a is a_k+1＝a_k,b_k+1＝μ_k,μ_k+1＝λ_k,λ_k+1＝a_k+1+0.382(b_k+1-a_k+1) Calculating a function value f₁＝f([λ_k+1]) Go to step 3.8;

step 3.8: setting k: if k +1, go to step 3.4;

the cluster number range obtained finally by the one-dimensional search is recorded as [ a ]_k,b_k]Therefore, the median value in this range is taken as the optimal cluster number:

the optimal cluster number is rounded down.

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